The present invention generally relates to methods of designing skeleton and plate structures, and more particularly to a method of designing optimum skeleton and plate structures which uses a computer to obtain more realistic skeleton and plate structures from a density distribution which is obtained as an optimum shape of a mechanical structure by a conventional shape optimizing design.
According to the conventional shape optimizing design (or modeling), the optimum shape of the mechanical structure is obtained in the following manner by use of the computer.
(1) For example, a rectangle is given as a design region in the case of 2 dimensions, and a rectangular parallelopiped is given as the design region in the case of 3 dimensions.
(2) The design region is divided into finite elements E.sub.i, where i=1, . . . , N, densities D.sub.i are given to the finite elements E.sub.i, and the densities D.sub.i or parameters thereof are set as design variables.
(3) Load conditions, support conditions and a total volume VT are given as restricting conditions with respect to the design region. The load conditions include points or regions where the load is applied, the magnitude of the load, and the direction of the load. The support conditions include points or regions where the support takes place, and support methods such as movable, rotatable and restriction. The total volume VT is a volume integral (integration value) of the density within the design region. An external force is applied to each of the load points and support points.
(4) A density distribution within the design region is obtained for a case where a target function f which is a function of the design variables becomes a maximum or a minimum.
(5) A shape which is obtained by eliminating the finite elements having a density which is 0 or a density less than a predetermined value is smoothened by a Bezier curve so as to obtain an optimum shape.
As specific techniques for making the shape optimizing design, there are techniques which use a homogenization method. For example, such a technique using the homogenization method is proposed in Suzuki et al., "A Homogenization Method for Shape and Topology Optimization", Computer Methods in Applied Mechanics and Engineering, 1991.
A description will be given of this proposed technique using the homogenization method. In the case of 2 dimensions, a large number of small rectangular holes are formed in a design region as shown in FIG. 1A, and it is assumed that the rectangular holes are arranged regularly. The finite element E.sub.i is made up of one or a plurality of unit cells UC.sub.i shown in FIG. 1B, and each unit cell UC.sub.i is a square having sides with a length "1" and includes the rectangular hole having a size of a.sub.i xb.sub.i. The density D.sub.i of the finite element E.sub.i is equal to the density of the unit cell UC.sub.i, and is described by the following formula. EQU D.sub.i =1-a.sub.i .multidot.b.sub.i
In general, the design variables are the lengths a.sub.i and b.sub.i of the sides of the rectangular hole and an inclination .theta..sub.i, where i=1, . . . , N. The target function f is described by the following average compliance, where F denotes an external force, u denotes a displacement satisfying the principle of a virtual work, V denotes a volume (integration variable) and the integration range is the design region. EQU f=.intg.FudV
The displacement u is dependent on a resilient tensor of the finite element E.sub.i. It is assumed that the resilient tensor of the finite element E.sub.i is equal to the resilient tensor for the case where the finite element E.sub.i is replaced by a plate having a uniform density.
A density distribution having a maximum rigidity is obtained when the average compliance becomes a minimum under the given total volume VT. In the case of 3 dimensions, it is basically the same for the case of the 2 dimensions described above.
However, according to the conventional shape optimizing design, it was impossible to obtain the skeleton structure by the 2 or 3 dimensional design and the plate structure by the 3 dimensional design. Hence, the conventional shape optimizing design merely provided hints to the designer as to the shape, and considerable time was required until a final shape design is made.